BFS检查图表是否是c ++中的二分图

Question

我正在实现一种算法来确定无向图是否为二分图.基于这个伪代码制作了我的实现,它适用于连接的图形,但是当它被断开时,只是程序指示错误的答案.我认为如果它没有连接,那么每个不相交的子图需要一个循环.但我坚持这一点.我如何能够为我打印正确答案的代码？

#include <cstdio>
#include <vector>
#include <queue>
#include <iostream>
using namespace std;

#define MAX 1000

int numberVertex, numberEdges;
int particion[MAX], visited[MAX];
vector< int > adjacencyMatrix[MAX];

bool bfs()
{
    int i, origin, destination, begin;
    queue< int > queueVertex;
    begin = 0;
    queueVertex.push(begin);
    particion[begin] = 1; // 1 left,
    visited[begin] = 1; // set adjacencyMatrixray

    while(!queueVertex.empty())
    {
        origin = queueVertex.front(); queueVertex.pop();
        for(i=0; i < adjacencyMatrix[origin].size(); i++)
        {
            destination = adjacencyMatrix[origin][i];
            if(particion[origin] == particion[destination])
            {
                return false;
            }
            if(visited[destination] == 0)
            {
                visited[destination] = 1;
                particion[destination] = 3 - particion[origin]; // alter 1 and 2 subsets
                queueVertex.push(destination);
            }
        }
    }
    return true;
}

int main()
{
 freopen("tarea2.in", "r", stdin);
    int i,j, nodeOrigin, nodeDestination;
    scanf("%d %d", &numberVertex, &numberEdges);
    for(i=0; i<numberEdges; i++)
    {
        scanf("%d %d", &nodeOrigin, &nodeDestination);
        adjacencyMatrix[nodeOrigin].push_back(nodeDestination);
        adjacencyMatrix[nodeDestination].push_back(nodeOrigin);
    }
    if(bfs()) {

        printf("Is bipartite\n");
          for (j=0; j<numberVertex; j++){
        cout<<j<<" "<<particion[j]<<endl;
        }

    }
    else {printf("Is not bipartite\n");}





    return 0;
}

例如,对于此输入

6 4
3 0
1 0
2 5
5 4

输出应该是:

Is bipartite
0 1
1 2
2 1
3 2
4 1
5 2

而是抛出输出:

0 1
1 2
2 0
3 2
4 0
5 0

发生这种情况是因为图形不是连接的图形,即有两个连接的组件.我希望你能帮助我,因为我已经坚持了几天.

Answer 1

您应该在每个连接的组件上运行bfs.最简单的方法是迭代所有顶点,如果没有访问它们,那么只需在它们上调用bfs即可.

bool is_bipartite()
{
    for(int i = 0; i < numberVertex; i++)
    {
       if (visited[i] == 0 && !bfs(i)) {
           return false;
       }
    } 
    return true;
}

它仍然是线性的,因为您在每个连接的组件上运行一次bfs.

#include <cstdio>
#include <vector>
#include <queue>
#include <iostream>
using namespace std;

#define MAX 1000

int numberVertex, numberEdges;
int particion[MAX], visited[MAX];
vector< int > adjacencyMatrix[MAX];

bool bfs(int begin)
{
    int i, origin, destination;
    queue< int > queueVertex;
    queueVertex.push(begin);
    particion[begin] = 1; // 1 left,
    visited[begin] = 1; // set adjacencyMatrixray

    while(!queueVertex.empty())
    {
        origin = queueVertex.front(); queueVertex.pop();
        for(i=0; i < adjacencyMatrix[origin].size(); i++)
        {
            destination = adjacencyMatrix[origin][i];
            if(particion[origin] == particion[destination])
            {
                return false;
            }
            if(visited[destination] == 0)
            {
                visited[destination] = 1;
                particion[destination] = 3 - particion[origin]; // alter 1 and 2 subsets
                queueVertex.push(destination);
            }
        }
    }
    return true;
}

bool is_bipartite()
{
    for(int i=0; i< numberVertex; i++)
    {
       if (visited[i] == 0 && !bfs(i)) {
           return false;
       }
    } 
    return true;
}

int main()
{
    //freopen("tarea2.in", "r", stdin);
    int i,j, nodeOrigin, nodeDestination;
    scanf("%d %d", &numberVertex, &numberEdges);
    for(i=0; i<numberEdges; i++)
    {
        scanf("%d %d", &nodeOrigin, &nodeDestination);
        adjacencyMatrix[nodeOrigin].push_back(nodeDestination);
        adjacencyMatrix[nodeDestination].push_back(nodeOrigin);
    }
    if(is_bipartite()) {

        printf("Is bipartite\n");
          for (j=0; j<numberVertex; j++){
        cout<<j<<" "<<particion[j]<<endl;
        }

    }
    else {printf("Is not bipartite\n");}

    return 0;
}